par Quesne, Christiane 
Référence International journal of theoretical physics, 43, 2, page (545-559)
Publication Publié, 2004-02
Référence International journal of theoretical physics, 43, 2, page (545-559)
Publication Publié, 2004-02
Article révisé par les pairs
| Résumé : | We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, Eq (A + B) = Eq α0 (A) Eqα1 (B) ∏i=2∞ Eqα2 (C i). By systematically transforming the q-exponentials into exponentials of series and using the conventional Baker-Campbell-Hausdorff formula, we prove that one can make any choice for the bases q α2, i = 0, 1, 2, ..., of the q-exponentials in the infinite product. An explicit calculation of the operators Ci in the successive factors, carried out up to sixth order, also shows that the simplest q-Zassenhaus formula is obtained for α0 = α1 = 1, and α2 = 2, and α3 = 3. This confirms and reinforces a result of Sridhar and Jagannathan, on the basis of fourth-order calculations. |
